Leading universities in cities such as Edinburgh, Manchester, Bristol and Newcastle are at risk of losing their reputations as being among the best in the world to study for a degree, research suggests.

The "golden triangle" of Oxford, Cambridge and London is fast becoming Britain's last bastion of world class education and research, according to new international rankings.

The latest Times Higher Education World University Rankings for 2013/14 show that overall, the UK is holding its position, with 31 institutions in the top 200, more than any other country except the United States.

But a number of institutions outside London and Oxbridge have dropped down the table.

The rankings rate universities worldwide on 13 measures including teaching, research and their international outlook, which includes the number of overseas students and staff they have.

The UK has three universities in the top 10, with Oxford taking second place alongside Harvard in the US.

Cambridge University was seventh, and Imperial College London took tenth place.

There were seven UK universities in the top 50, and 11 in the top 100, up one from 10 last year.

London had four institutions in the top 40, compared with three last year, more than any other city in the world.

These were Imperial College, which was down two places to 10th; University College London, which fell four places to 21st; London School of Economics and Political Science (LSE), up seven places to 32nd; and King's College London, which rose 19 places to 38th.

Other London institutions to rise included Royal Holloway, University of London, up from 119th to 102nd, and Queen Mary, University of London which took 114th spot.

But a number of leading UK institutions fared less well, the rankings show.

Since the 2011/12 tables, Manchester has fallen from 48th to 58th, Bristol has gone from 66th to 79th, Sheffield from 101st to 112th, Aberdeen from 151st to 188th, Reading from 164th to 194th and Newcastle from 146th to 198th.

Since last year, Nottingham has gone from from 120th to 157th, Southampton from 130th to 146th and Warwick from 124th to 141st.

Top of this year's rankings was the California Institute of Technology, which was in first place for the third year running.

The rest of the top 10 was made up of Oxford and Harvard in joint second place, Stanford University in fourth, Massachussetts Institute of Technology, (5), Princeton (6), Cambridge (7), University of California, Berkeley (8), University of Chicago (9), Imperial College London (10).

Phil Baty, editor of the rankings, said: "On the whole, the UK has had a very stable year, with little overall change to its position behind the US as the world's second best higher education nation. This is good news after stark evidence of decline in last year's rankings.

"But there are still concerns for our world-leading 'brand name' institutions: Imperial College London, University College London plus the universities of Manchester and Bristol have all slipped to varying degrees. Although other institutions have risen, and some significantly, such global brands act as flagships for the rest of the UK, so this is a worry."

Scottish Education Secretary Mike Russell said: " Scottish universities are known at home and abroad for their excellence and this is highlighted by the fact that five of our universities feature in these international rankings. Scotland has the most universities per head of population which clearly shows we continue to excel and build on our unrivalled record of success."

He added that the Scottish Government's " substantial investment" of more than £1 billion a year in higher education was "paying off and, most importantly, delivering exceptional opportunities for students and employers".

Mr Russell added: " Earlier this year we announced additional funding, based on the levels of world leading research. I am sure the commitment and dedication of our universities and their staff, helped by our funding, will ensure our higher education system continues to go from strength to strength."

Professor Sir Christopher Snowden, president of vice-chancellors' group Universities UK, said: "This table, and other rankings, shows that the UK continues to possess, by some margin, the second-strongest university system in the world after the US.

"Such rankings, however, cannot tell the whole story about the strength of our sector. Universities' positions will vary from one international table to the next and this is just a small snapshot of all our universities' activities.

"What is clear, however, is that the UK must continue to invest in higher education if we are to maintain this global competitiveness."

Dr Wendy Piatt, director general of the Russell Group, which represents 24 leading universities including Oxford and Cambridge said: " With 11 universities in the top 100, we are second-only to the US and the UK still outflanks the majority of its competitors.

"The Government was right to protect research spending and talk up the importance of science and research for the UK's future growth.

"But investment in the UK still lags far behind the US, China and many other Western European countries. And the global race is hotting up - with many Asian universities continuing to climb up the rankings."

Sir David Bell, vice-chancellor of Reading University said: "No university can rest on its laurels. No one is guaranteed to retain a top-200 place when the US, Far East and others are investing in research so heavily.

"There are some dramatic year-on-year rises and falls this year, so we should be careful to read too much into a single set of figures,

"It is no surprise that a small number of UK universities at the very top end will remain more stable, with others more likely to fluctuate.

"We've got to be realistic. Research-intensive universities just below the leading institutions are in a very tight, crowded and turbulent international market. Gaining ground becomes tougher every year."